Book Titles Curvature Problems

		Curvature Problems by Claus Gerhardt
		ISBN-10: 1-57146-162-0 ISBN-13: 978-1-57146-162-9 Year Published: 2007 Pages: 323 pages Binding: Hardcover List Price: $79.00

Description:

Applying analytic methods to geometric problems has proved to be extremely fruitful in the last decades. Among the new techniques, with the help of which many problems have been solved, curvature flows and a priori estimates for fully non-linear elliptic partial differential equations are especially important. In this book, the author considers curvature problems in Riemannian and Lorentzian geometry which have in common either that the extrinsic curvature of closed hypersurfaces is prescribed or that curvature flows driven by the extrinsic curvature are studied and used to obtain some insight in the nature of possible singularities. This book will serve as an advanced textbook for graduate students and researchers interested in geometry and general relativity.

Table of Contents:

1. Foundations
2. Curvature flows in semi-Riemannian manifolds
3. Hypersurfaces of prescribed curvature in Riemannian manifolds
4. Hypersurfaces of prescribed curvature in Lorentzian manifolds
5. Hypersurfaces of prescribed scalar curvature
6. The IMCF in cosmological spacetimes
7. The IMCF in ARW spaces
8. The IMCF in Robertson-Walker spaces
9. Minkowski type problems in Sⁿ⁺¹
10. Minkowski type problems in Hⁿ⁺¹

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